发表机构
Research Center for Pre-Disease Science, University of Toyama（富山大学疾病前科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从局部线性近似视角重新解释Brunner-Munzel检验统计量，推导其方差估计量，以帮助实践者直观理解并放心使用该非参数检验。
AI 中文摘要
Brunner-Munzel (BM)检验是一种用于两个独立样本的非参数检验，它评估一组观测值是否倾向于大于另一组观测值，或反之。BM检验比Mann-Whitney $U$检验具有更广泛的应用范围，因为它不假设两组之间的方差相等。然而，BM检验统计量的含义难以直观理解，这可能是阻碍BM检验广泛使用的因素之一。为缓解这一问题，本文从局部线性近似的视角引入了BM检验统计量的一种替代解释。结果表明，BM检验中使用的样本随机优势的方差估计量可以通过局部线性近似推导出来，其中每个观测值对样本随机优势的影响被假定为可加的。这一简单解释将有助于实践者毫不犹豫地决定使用BM检验。
英文摘要
The Brunner-Munzel (BM) test is a nonparametric test for two independent samples that evaluates whether observations from one group tend to be greater than observations from another group, or vice versa. The BM test has a broader scope of application than the Mann-Whitney $U$ test because it does not assume equal variances between the two groups. However, the meaning of the BM test statistic is difficult to understand intuitively, which may be one of the factors hindering the widespread use of the BM test. To alleviate this problem, in this paper, I introduce an alternative interpretation of the BM test statistic from the viewpoint of local linear approximation. It is shown that the variance estimator for the sample stochastic superiority used in the BM test can be derived using local linear approximation, in which the influence of each observation on the sample stochastic superiority is assumed to be additive. This simple interpretation will help practitioners decide to use the BM test without hesitation.
Comments17 pages, 9 figures
